I've been learning SQL and I wanted some data to play around with and I thought it would be fun if I used TM server data from a popular server like SpeedMania. User rank, times on different tracks, etc. Is that possible to do? If so, how would I do it? I'm gonna be using MySQL if that makes a difference (still learning how to work with that).

Longer answer:
Access to a dedicated server's XML-RPC port is only possible if that server's admin has allowed it for public connections, but that would be Really Bad Practice™.
Access to a server's controller data is generally not possible either as no controller comes with an public API for that sort of thing (AFAIK). The closest thing might be a website displaying some controller data, or a third-party plugin making some data available, but again, the server admin controls that.

For learning MySQL, setting up your own server with a MySQL-based controller (such as XAseco) and then fooling around with that, would be a more viable approach.